Republican Marsha Blackburn has surged to an 8-point lead over Democrat Phil Bredesen in a new CBS poll of Tennessee's U.S Senate race — a bounce that coincides with the nation's furious debate over the confirmation of Supreme Court Justice Brett Kavanaugh.

The poll, released Sunday, found Blackburn, a conservative Williamson County congressman, with support from 50 percent of registered voters in Tennessee, compared to 42 percent for Bredesen, a former two-term Tennessee governor.

It comes as the pollster says this race and others where Democrats are seeking to win in traditionally Republican states have "nationalized." The collection of polls in Tennessee, Arizona and Texas found Democrats with "at best mixed results."

Blackburn is seeking to replace the retiring U.S. Sen. Bob Corker in a closely contested campaign, and her lead is the largest any public poll has placed her at since the Aug. 2 primary.

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The CBS News 2018 Battleground Tracker poll, a survey of 1,002 registered voters taken between Oct. 2 and Oct. 5, has a margin of error of 3.4 percentage points. The poll was conducted by YouGov, an online polling company.

"By more than two to one, registered voters say national issues outweigh local ones, and voters in all the states surveyed say their vote for the Senate is mainly about the direction of the country over a list of other factors," a CBS analysis of the poll reads.

The CBS poll follows a new Fox News poll last week showed Blackburn ahead by 48 percent to 43 percent, which together suggests a possible shift in the race.

Michael Anastasi, vice president of news for the USA TODAY NETWORK - Tennessee, steps up to the podium to deliver opening remarks at the 2018 Tennessee U.S. Senate Debate at Cumberland University Tuesday, Sept. 25, 2018, in Lebanon, Tenn. Lacy Atkins / The Tennessean

Moderators David Plazas, left, of The Tennessean, and Rhori Johnson, of NewsChannel 5, speak to the audience at the 2018 Tennessee U.S. Senate Debate at Cumberland University Tuesday, Sept. 25, 2018, in Lebanon, Tenn. Lacy Atkins / The Tennessean

Marsha Blackburn supporters move into position in anticipation of her arrival for the 2018 Tennessee U.S. Senate Debate at Cumberland University Tuesday, Sept. 25, 2018, in Lebanon, Tenn. Larry McCormack / The Tennessean

Democratic candidate Phil Bredesen and his wife Andrea Conte walk through a crowd of supporters before the 2018 Tennessee U.S. Senate Debate at Cumberland University Tuesday, Sept. 25, 2018, in Lebanon, Tenn. Larry McCormack / The Tennessean

The Lebanon High School band arrives to play for Phil Bredesen supporters outside the 2018 Tennessee U.S. Senate Debate at Cumberland University Tuesday, Sept. 25, 2018, in Lebanon, Tenn. Larry McCormack / The Tennessean

Phil Bredesen supporters listen to the Lebanon High School band before the start of the 2018 Tennessee U.S. Senate Debate at Cumberland University Tuesday, Sept. 25, 2018, in Lebanon, Tenn. Larry McCormack / The Tennessean

In Tennessee, 44 percent of respondents in the CBS poll said their Senate vote would be in support of President Donald Trump, while only 26 percent said it would be in opposition of him. Just 30 percent said their vote would not be about Trump.

The poll was taken at the height of the partisan fight over Kavanaugh's nomination after Christine Blasey Ford testified on Sept. 27 that Kavanaugh sexually assaulted her while they were in high school. Republicans slammed the allegations as a political stunt orchestrated by Democrats, and the Senate voted 50-48 to confirm Kavanaugh on Saturday, largely along party lines.

The poll found that in Tennessee — where Trump won overwhelmingly in 2016 — 47 percent of respondents supported the confirmation of Kavanaugh compared to 30 percent who opposed it.

"In Tennessee and Texas, where Republicans lead, more voters wanted the Senate to confirm Brett Kavanaugh than not," the analysis says.

"In each state, views on Kavanaugh divide along partisan lines, with three in four Republicans supporting confirmation, and between six and seven in ten Democrats opposing it."

Blackburn came out immediately in support of Kavanaugh's confirmation while Bredesen waited until this past Friday to say he backed Trump's pick for the Supreme Court, bucking his party on the issue.

Bredesen said he had held off giving his yes-or-no position on Kavanaugh to study Kavanaugh's hearings and later watch Ford's testimony, but his delay was attacked repeatedly by Blackburn.

Fifty-five percent of Tennessee respondents said Kavanaugh's nomination makes them more motivated to go to the polls to vote in November.

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